Reducing shimmy oscillation of nose landing gear based on a torsional nonlinear energy sink and an annular granular damper

Shimmy in nose landing gears may induce high-cycle fatigue in critical structural components and thus poses a safety risk during taxiing, take-off, and landing rollouts. To mitigate shimmy under complex service conditions, this study proposes a passive hybrid suppression concept by integrating a torsional nonlinear energy sink (NES) and an annular granular particle damper (PD) into a single-wheel nose landing gear system. A coupled nonlinear shimmy model involving torsional and lateral bending modes is developed based on the Thota tire force formulation and stretched-string tire deformation dynamics, with geometric effects induced by the rake angle also considered. The torsional NES is realized through a modified roller–spring mechanism, whose nonlinear restoring torque is derived via geometric analysis and cubic Taylor approximation, resulting in near-zero linear stiffness with a positive cubic stiffness component. The annular PD is modeled using a gas–solid two-phase-flow-based equivalent viscous damping approach, and the corresponding torsional damping torque is incorporated into the governing equations. Bifurcation analyses are performed using MATCONT in the (V, Fz)-plane to evaluate the stability boundaries and the oscillation regions of torsional shimmy, lateral bending shimmy, and bistability. The results show that the standalone NES effectively reduces the torsional shimmy region and enlarges the stable domain in the low-load range. In contrast, the standalone PD significantly attenuates vibration amplitudes but enlarges the shimmy region and induces a characteristic “Both” oscillation mode in which torsional and lateral responses coexist. The combined NES–PD configuration simultaneously achieves substantial amplitude reduction and a contraction of the unstable operating region. For a representative low-load case, the maximum torsional amplitude is reduced by about 87% compared with the baseline configuration, while the shimmy speed interval is also decreased. A parametric study is further conducted to evaluate the influence of key NES and PD parameters, including the concave track radius, spring pre-stretch, spring stiffness, roller radius, particle filling ratio, and particle density, on the shimmy suppression performance.